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The group of functions from an object G to itself which preserve the structure of the object, denoted Aut(G). The automorphism group of a group preserves the multiplication ...

A line segment joining the midpoints of opposite sides of a quadrilateral or tetrahedron. Varignon's theorem states that the bimedians of a quadrilateral bisect each other ...

A binary operation f(x,y) is an operation that applies to two quantities or expressions x and y. A binary operation on a nonempty set A is a map f:A×A->A such that 1. f is ...

The number of single operations (of addition, subtraction, and multiplication) required to complete an algorithm.

A number n for which a shortest chain exists which is a Brauer chain is called a Brauer number. There are infinitely many non-Brauer numbers.

Two elements x and y of a set S are said to be commutative under a binary operation * if they satisfy x*y=y*x. (1) Real numbers are commutative under addition x+y=y+x (2) and ...

The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...

The difference of two complex numbers z=x+iy and z^'=x^'+iy^' is given by z-z^'=(x-x^')+i(y-y^'). In component form, (x,y)-(x^',y^')=(x-x^',y-y^').

The closed cyclic self-intersecting hexagon formed by joining the adjacent antiparallels in the construction of the cosine circle. The sides of this hexagon have the property ...

The direction from an object A to another object B can be specified as a vector v=AB^-> with tail at A and head at B. However, since this vector has length equal to the ...